Numerical simulations of thermally forced 2-D flows in idealized valley cross-sections

This paper focuses on the free convective circulations that develop in a valley cross-section in response to the heat exchanges between soil and the valley atmosphere. Studies of this kind are of basic importance in the field of pollutants dispersion over complex topographies. The considered conditions are those characterizing the diurnal transition period, when the along-valley wind is not yet fully developed and, to a certain degree of approximation, the atmospheric circulation developing in the valley can be viewed as a 2-D motion, perpendicular to the valley axis. Furthermore, during the diurnal transition period, both the topography and the stable temperature stratification act to inhibit the exchanges of mass and energy between the valley atmosphere and the overlying free atmosphere, confining the motion into the valley itself.

All the numerical experiments were conducted on simple trapezoidal domains, with different shapes and dimensions (heights and widths ranging from 495 to 1000 and from 2500 to 7800 meters respectively). Since the upper closure of these trapezoidal cavities with rigid lids constitutes a somewhat unrealistic boundary condition (preventing at all exchanges between the valley atmosphere and the free atmosphere), in some calculations the domains were extended, adding large rectangular regions above the top of the aforementioned trapezia. The flow has always been initialized with zero velocity everywhere and stable temperature stratification (using different Brunt-Väisälä frequencies). Two different scenarios, concerning the boundary conditions at the valleys side-walls and bottoms (being all the remaining walls adiabatic), were considered: a) cavity with side-walls kept at different (but constant in time) temperatures; b) cavity with different (but constant in time) heat fluxes at the side-walls and bottom. The conditions of point a) attempt to reproduce the situation arising when, because of the valley orientation, one slope receives direct solar radiation and the other one is in shade, while those of point b) refer to uniform surface heating.

The numerical simulations were carried on (using the Boussinesq approximation) with a general purpose finite-volumes solver of the Navier-Stokes equations (STAR-CD version 3.1). Before employing it in the simulations presented in this paper, the program has been extensively and accurately tested. Turbulence was modeled with the standard k-e model, varying its principal parameters in accordance to the ranges found in literature. Major conclusions arising from this study are the following: 1) the main characteristics of the simulated flows (particularly concerning the kinematical and thermal structures of the slope wind layers and the vertical temperature distributions in the valleys core regions) show reasonable agreement with analogous observed and simulated atmospheric circulations, thus encouraging, at least in a first approach at the quantitative study of the problem, to use the proposed model (also in conjunction with more complex and realistic geometries and boundary conditions); 2) at least for the simple geometries and boundary conditions analyzed, the model has shown low sensitivity to the investigated variations in the k-e model parameters and to the previously described changes in the domains shape to account for the influence of the free-atmosphere on the valley circulation.